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PLEASE SIR SOLVE THE PROBLEM BY USING INTEGRATION OR USING SOME STANDARD RESULT AS I CANT UNDERSTAND THE SOLUTION GIVEN BY ALL ONLINE COACHING CENTER SOLUTIONS.PLEASE HELP SIR.HERE IS THE LINK http://www.goiit.com/posts/list/mechanics-solve-it-1015155.htm
Derivation Of Electric Field Due to One Hemisphere.
σ=Q/2πR²
4π Solid Angle Corresponds To Q/ε0 Flux.............................From Gauss's Theorem
2π Solid Angle Will Correspond To Q/2ε0 Flux
Q/2ε0=E2πR²
E=Q/(2ε02πR²)
E=σ/2ε0
Force= F= Edq..........................(F applied will be used to counteract this force)
dq=dAσ
F=(σ/2ε0)(dAσ)
P=F/dA=σ²/2ε0
Force Due To One Hemisphere On Other
=PπR².........................(πR² because we are calculating force on the rim of other hemisphere)
=(σ²/2ε0)πR²
=πR²σ²/2ε0
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